3.1.1 Linear Model

model<-lm(Global_Sales~Critic_Score+User_Score+Genre+Year_of_Release,data=trainData)

summary(model)

## 
## Call:
## lm(formula = Global_Sales ~ Critic_Score + User_Score + Genre + 
##     Year_of_Release, data = trainData)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.64127 -0.25745 -0.09946  0.15256  1.49087 
## 
## Coefficients:
##                     Estimate Std. Error t value Pr(>|t|)    
## (Intercept)        1.7500247  2.7185929   0.644  0.51978    
## Critic_Score       0.0094591  0.0004970  19.034  < 2e-16 ***
## User_Score        -0.0096350  0.0047565  -2.026  0.04285 *  
## GenreAdventure    -0.1413698  0.0287138  -4.923 8.78e-07 ***
## GenreFighting      0.0330152  0.0252321   1.308  0.19078    
## GenreMisc          0.0260103  0.0254548   1.022  0.30691    
## GenrePlatform      0.0026508  0.0249682   0.106  0.91545    
## GenrePuzzle       -0.1322916  0.0417685  -3.167  0.00155 ** 
## GenreRacing       -0.0142833  0.0213105  -0.670  0.50273    
## GenreRole-Playing -0.0807471  0.0197866  -4.081 4.56e-05 ***
## GenreShooter      -0.0135506  0.0186155  -0.728  0.46670    
## GenreSimulation   -0.0345418  0.0280356  -1.232  0.21798    
## GenreSports       -0.0092711  0.0184109  -0.504  0.61459    
## GenreStrategy     -0.2303472  0.0278174  -8.281  < 2e-16 ***
## Year_of_Release   -0.0009515  0.0013517  -0.704  0.48149    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3717 on 4904 degrees of freedom
## Multiple R-squared:  0.1131, Adjusted R-squared:  0.1106 
## F-statistic: 44.68 on 14 and 4904 DF,  p-value: < 2.2e-16

The model aims to predict a dependent variable, likely related to video game sales, based on various independent variables like User_score,Critic_score,Genre and year of release

Coefficient The coefficients indicate the impact of each independent variable on the dependent variable. The independent variables in the model such as Critic_Score,User_Score, and GenreStrategy have significant effects on video game sales

R square The R-squared value (0.1131) indicates that the model explains approximately 11.31% of the variance in the dependent variable.

Adj R Square The adjusted R-squared (0.1106) accounts for the number of predictors in the model.

An R-squared value of -3.385177 is unusual.Negative R-squared values usually suggest that the model is performing worse than the Null model.Based on this R-squared value, the model is not considered good for explaining the variability in Global_Sales.

residuals <- model$residuals
hist(residuals, breaks = 30, main = "Histogram of Residuals", xlab = "Residuals", col = "blue")
abline(v = mean(residuals), col = "red", lwd = 2)

In the graph we could see that the residuals are normaly distributed stating the assumptions of linear Regression model

3.2.1 Logistic Model

# Fit a logistic regression model
logit_model <- glm(Hit ~ Critic_Score + Developer  + Genre , 
                   data = train_data, family = binomial())
print(summary(logit_model))

## 
## Call:
## glm(formula = Hit ~ Critic_Score + Developer + Genre, family = binomial(), 
##     data = train_data)
## 
## Coefficients:
##                    Estimate Std. Error z value Pr(>|z|)    
## (Intercept)       -4.639119   0.381704 -12.154  < 2e-16 ***
## Critic_Score       0.053450   0.003159  16.921  < 2e-16 ***
## Developer1553      0.309054   0.422558   0.731  0.46454    
## Developer1561      0.390173   0.435695   0.896  0.37051    
## Developer266      -0.145614   0.408228  -0.357  0.72132    
## Developer307      -0.492524   0.489739  -1.006  0.31457    
## Developer434      -0.130454   0.405546  -0.322  0.74770    
## Developer452       0.556586   0.407152   1.367  0.17162    
## Developer456       0.865595   0.435744   1.986  0.04698 *  
## Developer480       0.516676   0.449320   1.150  0.25018    
## Developer827      -0.289683   0.436706  -0.663  0.50712    
## DeveloperOthers   -0.131287   0.329242  -0.399  0.69007    
## GenreAdventure    -0.960955   0.242681  -3.960 7.50e-05 ***
## GenreFighting     -0.061046   0.160102  -0.381  0.70299    
## GenreMisc          0.003359   0.161289   0.021  0.98338    
## GenrePlatform      0.006520   0.158578   0.041  0.96720    
## GenrePuzzle       -0.824972   0.318277  -2.592  0.00954 ** 
## GenreRacing       -0.135961   0.143275  -0.949  0.34265    
## GenreRole-Playing -0.344525   0.129743  -2.655  0.00792 ** 
## GenreShooter       0.023498   0.118709   0.198  0.84309    
## GenreSimulation   -0.325123   0.183257  -1.774  0.07604 .  
## GenreSports       -0.210337   0.127580  -1.649  0.09922 .  
## GenreStrategy     -1.142691   0.222714  -5.131 2.89e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 5558.4  on 4917  degrees of freedom
## Residual deviance: 5104.6  on 4895  degrees of freedom
## AIC: 5150.6
## 
## Number of Fisher Scoring iterations: 4

# Plot the ROC curve
plot(roc_obj, main = "ROC Curve for Logistic Regression Model")

# Print AUC (Area Under the Curve)
#auc(roc_obj)

Area under the curve: 0.7107

# Assuming you have 'predictions' and 'test_data$Hit' from your logistic regression model
predicted_class <- ifelse(predictions > 0.5, "1", "0")
predicted_class <- factor(predicted_class, levels = c("0", "1"))

# Actual values
actual_class <- test_data$Hit

# Create a table for Actual vs Predicted
confusion_matrix <- table(Predicted = predicted_class, Actual = actual_class)

library(ggplot2)

# Assuming you have 'predicted_class' and 'actual_class' from your model
# Convert the confusion matrix to a data frame for plotting
confusion_matrix_df <- as.data.frame(confusion_matrix)

# Rename columns
names(confusion_matrix_df) <- c("Predicted", "Actual", "Freq")

# Plot the confusion matrix using ggplot2
ggplot(data = confusion_matrix_df, aes(x = Actual, y = Predicted, fill = Freq)) +
  geom_tile(colour = "white") +
  scale_fill_gradient(low = "white", high = "blue") +
  geom_text(aes(label = sprintf("%0.0f", Freq)), vjust = 1) +
  theme_minimal() +
  labs(fill = "Frequency", x = "Actual Class", y = "Predicted Class", title = "Confusion Matrix")

We are using logistic regression model to predict if a games is hit or not based on the threshold value. we are using Critic Score , Developer and Genre as predicotrs. For making logistic model at first we are using binning function. Binning top developers because there are likely many unique developers in the dataset. Without binning, the model would have too many variables (one for each developer), many of which would have little data, leading to overfitting and making the model less generalizable. By binning, you reduce the complexity of the model and focus on the most common developers.

Coefficients and p-values: These values represent the change in the log odds of the dependent variable (in your case, whether a game is a ‘hit’ or not) for a one-unit change in the predictor.

Critic_Score (Coefficient: 0.053450, p-value: < 2e-16) * This is a highly significant predictor. The positive coefficient indicates that higher critic scores are associated with a higher likelihood of a game being a hit. The extremely low p-value suggests this relationship is statistically significant.

Developer456 (Coefficient: 0.865595, p-value: 0.04698)

• This specific developer (represented as ‘Developer456’) has a positive impact on the likelihood of a game being a hit. The p-value is just under 0.05, indicating that this result is statistically significant, although it’s on the borderline.

GenreAdventure (Coefficient: -0.960955, p-value: 7.50e-05)

• Being an adventure game is associated with a lower likelihood of being a hit, as indicated by the negative coefficient. The p-value is very small, showing strong evidence against the null hypothesis.

GenrePuzzle (Coefficient: -0.824972, p-value: 0.00954)

Puzzle games are also less likely to be hits. The negative coefficient and its low p-value signify a strong and statistically significant relationship.

GenreRole-Playing (Coefficient: -0.344525, p-value: 0.00792)

• Role-Playing games have a negative coefficient, suggesting they are less likely to be hits compared to the baseline genre. The p-value indicates this finding is statistically significant.

GenreStrategy (Coefficient: -1.142691, p-value: 2.89e-07)

• Strategy games show a strong negative association with being a hit. The coefficient is significantly negative, and the very low p-value strongly supports its significance.

Null Devience:

• Null deviance shows the goodness of fit of a model with no predictors (only the intercept) and residual deviance shows the goodness of fit of your model. A lower residual deviance compared to the null deviance indicates that the model is a better fit than the null model.

Accuracy(0.7606): * The above model has an accuracy of 76.06%, which means it correctly predicts whether a game is a hit or not 76.06% of the time.

Confusion Matrix:

• True Negatives (TN): 897 - The model correctly predicted the non-hit games.
• False Positives (FP): 273 - The model incorrectly predicted these games as hits.
• False Negatives (FN): 21 - The model incorrectly predicted these hits as non-hits.
• True Positives (TP): 37 - The model correctly predicted the hit games.

Summary: Based on the provided information, the logistic regression model exhibits an overall accuracy of 76.06%, which is higher than the no information rate, suggesting it has learned to predict better than a naive model. However, the model has a high sensitivity (97.71%) and low specificity (11.94%), indicating it is adept at predicting games that will not be hits (flops) but performs poorly in identifying successful hit games. The Area Under the Curve (AUC) of 0.7107 from the ROC analysis reveals a good discriminatory ability, but the model’s prediction bias towards non-hits is also evident, as shown by the high number of false negatives. This suggests that while the model is quite conservative and effective in identifying non-hit games, it needs improvement to balance its predictive performance for both hits and non-hits

3.2.2 Decision Trees

rpart.plot(tree_model, extra = 101, under = TRUE, cex = 0.8)